The class of forward-flat systems has already been analyzed in detail
in the literature, see e.g. [1]}, [2]}
and [3]}. In [4]},
it has been shown that every forward-flat system can be decomposed
into a smaller dimensional forward-flat subsystem and an endogenous
dynamic feedback by a suitable state- and input-transformation. Thus,
a repeated decomposition allows to check whether a system is forward-flat
or not. In [5]}, this test has been formulated
in terms of certain sequences of distributions, similar to the test
for static-feedback linearizability in [6]}.
Thus, the property of forward-flatness can be checked in a computationally
efficient way. For flat systems that are not forward-flat, the decomposition
procedure as stated in [4]} necessarily
fails in one step, likewise the test as proposed in [5]}.
